WASHINGTON -- U.S. senators leaving a classified briefing on the deteriorating situation in Iraq held off on prescribing a specific action to stem the violence in Iraq, and said all options should be considered.

Even hawkish Republicans such as John McCain (Republican-Arizona), Lindsey Graham (Republican-South Carolina), and James Inhofe (Republican-Oklahoma) stopped short of calling on President Barack Obama to back air strikes, saying the decision was his and the military's.

"I want to hear from the president. I'm not the commander in chief. I'm tired of telling him what to do. It's not really my place to tell him what to do," Graham said. "As a Republican, if he believes he needs to use air power to change the battlefield equation, and our generals advise us that would occur, I would be willing to support it."

He did say that it was in the U.S. national security interest to intervene. "Absolutely. The people in the ISIS [Islamic State in Iraq and Greater Syria, and/or the Levant] have as part of their agenda to attack our homeland. The next 9/11 is in the making. Syria has become the Afghanistan before 9/11 -- it's a place for safe havens and training."

McCain said the president should "get rid of" his entire national-security team and bring in General David Petraeus and those who "won the conflict in Iraq." But he acknowledged that the situation would be "extremely difficult" to turn around.

"There are many options. The options that we have become fewer and fewer as the startling success of ISIS continues," he said. "Air strikes may be part of it. Airstrikes may not be a part of it. I would rely on their judgement," he said of the generals. "I am not calling for air strikes."

Inhofe said: "This is too early to have each one of us making our recommendations. We are in the process in making those determinations. We're not there yet."

The hesitancy of top Republicans to make a specific recommendation underscores the seriousness of the situation in Iraq.

Sunni Islamist rebels from the Islamic State in Iraq and the Levant (ISIL) have made a stunning advance on Iraq, gaining control of key cities including Mosul and Tikrit, north of Baghdad.

Iraqi Army soldiers have abandoned their posts and fled in several of those cities in the face of the violent insurgency.

Top Democrats also agreed that the administration should evaluate options. "All the options should be thoughtfully looked at -- we shouldn't knee-jerk anything," said Carl Levin (Democrat-Michigan), chairman of the Senate Committee on Armed Services.

On air strikes, Senator Joe Manchin (Democrat-West Virginia), said, "It might be the only way that we can go in and give some support so they can hold off until they can regroup."

On June 12, Obama said that all options are open to help Iraq fight the Islamist militants' advance.